Average Error: 6.3 → 0.2
Time: 9.8s
Precision: 64
\[\frac{k}{\left(\left(f \cdot f\right) \cdot f\right) \cdot f}\]
\[{f}^{-2} \cdot \frac{k}{{f}^{2}}\]
\frac{k}{\left(\left(f \cdot f\right) \cdot f\right) \cdot f}
{f}^{-2} \cdot \frac{k}{{f}^{2}}
double f(double k, double f) {
        double r1472864 = k;
        double r1472865 = f;
        double r1472866 = r1472865 * r1472865;
        double r1472867 = r1472866 * r1472865;
        double r1472868 = r1472867 * r1472865;
        double r1472869 = r1472864 / r1472868;
        return r1472869;
}

double f(double k, double f) {
        double r1472870 = f;
        double r1472871 = -2.0;
        double r1472872 = pow(r1472870, r1472871);
        double r1472873 = k;
        double r1472874 = 2.0;
        double r1472875 = pow(r1472870, r1472874);
        double r1472876 = r1472873 / r1472875;
        double r1472877 = r1472872 * r1472876;
        return r1472877;
}

Error

Bits error versus k

Bits error versus f

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 6.3

    \[\frac{k}{\left(\left(f \cdot f\right) \cdot f\right) \cdot f}\]
  2. Simplified6.2

    \[\leadsto \color{blue}{\frac{k}{{f}^{4}}}\]
  3. Using strategy rm
  4. Applied add-sqr-sqrt35.0

    \[\leadsto \frac{k}{{\color{blue}{\left(\sqrt{f} \cdot \sqrt{f}\right)}}^{4}}\]
  5. Applied unpow-prod-down35.1

    \[\leadsto \frac{k}{\color{blue}{{\left(\sqrt{f}\right)}^{4} \cdot {\left(\sqrt{f}\right)}^{4}}}\]
  6. Applied *-un-lft-identity35.1

    \[\leadsto \frac{\color{blue}{1 \cdot k}}{{\left(\sqrt{f}\right)}^{4} \cdot {\left(\sqrt{f}\right)}^{4}}\]
  7. Applied times-frac32.1

    \[\leadsto \color{blue}{\frac{1}{{\left(\sqrt{f}\right)}^{4}} \cdot \frac{k}{{\left(\sqrt{f}\right)}^{4}}}\]
  8. Simplified32.0

    \[\leadsto \color{blue}{\frac{1}{{f}^{2}}} \cdot \frac{k}{{\left(\sqrt{f}\right)}^{4}}\]
  9. Simplified0.2

    \[\leadsto \frac{1}{{f}^{2}} \cdot \color{blue}{\frac{k}{{f}^{2}}}\]
  10. Using strategy rm
  11. Applied pow-flip0.2

    \[\leadsto \color{blue}{{f}^{\left(-2\right)}} \cdot \frac{k}{{f}^{2}}\]
  12. Simplified0.2

    \[\leadsto {f}^{\color{blue}{-2}} \cdot \frac{k}{{f}^{2}}\]
  13. Final simplification0.2

    \[\leadsto {f}^{-2} \cdot \frac{k}{{f}^{2}}\]

Reproduce

herbie shell --seed 1 
(FPCore (k f)
  :name "k / (f*f*f*f)"
  :precision binary64
  (/ k (* (* (* f f) f) f)))